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GATE 2024 MA – Question 7

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

Seven identical cylindrical chalk sticks fit tightly in a cylindrical container as shown. Container and sticks have equal length. Find occupied-space/empty-space ratio.

Diagram for GATE 2024 MA question 7
  1. 5/2
  2. 7/2
  3. 9/2
  4. 3

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Show answer and explanation

Correct answer: (B) 7/2

Explanation

Let stick radius be r. The six outer centers are 2r from the center, so container radius is 3r. Total cross-section =9πr², occupied=7πr², empty=2πr². Common length cancels; ratio **7/2, B**.

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